Bending moment

About: Bending moment is a research topic. Over the lifetime, 14577 publications have been published within this topic receiving 158834 citations. The topic is also known as: bending moment.

A comparative study on empty and foam-filled hybrid material double-hat beams under lateral impact

Abstract: In previous research, an innovative hybrid material double-hat thin-walled beam has been proposed for vehicle bumper system, which has demonstrated great potentials for improved pedestrian safety and reduced weight. In this work, we have used aluminum foam to fill the hybrid double-hat beam to further its application in vehicle bodies with increased bending resistance and energy absorption efficiency. Bending behaviors of both empty and foam-filled hybrid beams were numerically investigated using the validated LS-DYNA models. Three representative loading positions including the mid-span, 50 mm and 100 mm offsets from the mid-span were simulated to reveal the effect of load position uncertainty. It was found that the foam filler could increase the specific energy absorption (SEA) by more than 30% and double the bending moment (Mb) of the empty hybrid beam by changing its deformation pattern. Moreover, the foam-filled beam shows more robust crashworthiness performance against load position variation. Using radial basis function (RBF) metamodels, the multi-objective design optimization (MDO) problems were formulated for both empty and filled hybrid beams to maximize SEA and Mb and minimize the initial peak force (Fip). The multi-objective particle swarm optimization (MOPSO) was used to seek the Pareto fronts of the MDO problems. The MDO results show that the foam-filled beam has much broader performance space in terms of Fip, SEA and Mb and has great potentials for high-energy crash applications. It was also found that the Pareto front varies for different loading positions for either empty or filled hybrid beam. Including multiple loading positions could achieve a more robust design against load uncertainty. Appropriate weighting factors should be chosen for different loading positions to yield realistic and more robust designs of the proposed hybrid beams.

A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates

Abstract: This is the first paper of a pair which together discuss the development of a class of overlapping hinged bending finite elements which are suitable for the analysis of thin-shell, plate and beam structures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based on quadratic overlapping assumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher-order nodal variables. In this paper the hinged bending element concept is introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements are formulated. In paper II these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin-shell structures.

A simplified formulation of adhesion problems with elastic plates

Abstract: The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.